In this paper, we propose a superimposed training based two-phase robust channel estimation scheme for the unmanned aerial vehicle (UAV) assisted cellular communication system, in which various unitarily-invariant channel statistics errors are considered. Specifically, in the first phase, mobile station (MS) estimates the UAV-MS channel via the UAV training sequence, of which the robust design can be solved based on convex-concave theory. While in the second phase, the superimposed training scheme is considered at the ground base station (GBS) to improve spectrum efficiency. Then the robust GBS training sequence, the information signal power and the UAV amplifying factor are jointly optimized for the partially cascaded GBS-UAV-MS channel estimation subject to GBS and UAV transmit power constraints as well as the required information signal strength at the MS. To tackle this NP-hard problem, the optimal structures of involved variables are firstly derived, based on which the robust superimposed training design is simplified and proved to be quasi-convex in the UAV amplifying factor. Particularly, for Spectral norm and Nuclear norm bounded errors, the optimal training sequence can be obtained via convex-concave theory and Golden section searchWhile for Frobenius norm bounded error, a tractable upper-bounding scheme is proposed for the robust superimposed training design. Furthermore, we extend our work into the more general probabilistic path loss scenario of UAV-ground channels, and analyze the impacts of the probabilistic path loss and Rician $K$ -factor on channel estimation performance. Numerical results illustrate the excellent performance of the proposed superimposed training based two-phase channel estimation scheme.

中文翻译：

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无人机辅助通信系统鲁棒叠加训练优化

在本文中，我们为无人机（UAV）辅助蜂窝通信系统提出了一种基于叠加训练的两阶段鲁棒信道估计方案，其中考虑了各种单一不变的信道统计误差。具体来说，在第一阶段，移动台（MS）通过无人机训练序列估计无人机-MS信道，其鲁棒设计可以基于凸凹理论解决。而在第二阶段，地面基站（GBS）考虑叠加训练方案，以提高频谱效率。然后是稳健的 GBS 训练序列，信息信号功率和 UAV 放大系数针对部分级联 GBS-UAV-MS 信道估计进行联合优化，受 GBS 和 UAV 发射功率约束以及 MS 所需的信息信号强度。为了解决这个NP难题，首先推导出所涉及变量的最优结构，在此基础上简化了鲁棒叠加训练设计，并在无人机放大因子中证明是准凸的。特别是，对于谱范数和核范数有界误差，可以通过凸凹理论和黄金分割搜索获得最优训练序列，而对于 Frobenius 范数有界误差，提出了一种易于处理的上界方案，用于鲁棒叠加训练设计。此外，我们将我们的工作扩展到无人机地面信道的更一般的概率路径损耗场景，并分析概率路径损耗和 Rician $K$ 因子对信道估计性能的影响。数值结果说明了所提出的基于叠加训练的两相信道估计方案的优异性能。